If harmonic means of two random variables are equal, does arithmetic means of them are equal too?

Question

If there are two random variables whose harmonic means are equal,

does they have same arithmetic mean?

In other words,

If $E[\frac{1}{X}]=E[\frac{1}{Y}]$, then $E[X]=E[Y]$?

Assuming that we know their harmonic means and arithmetic means are non-zero.